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Vector Algebra

Question
CBSEENMA12033990
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Find a unit vector in the direction of straight a with rightwards arrow on top space equals space 3 space straight i with hat on top space minus space 2 space straight j with hat on top space plus space 6 space straight k with hat on top.

Solution

     straight a with rightwards arrow on top space equals space 3 straight i with hat on top space minus space space 2 straight j with hat on top space plus space 6 straight k with hat on top
therefore space space space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space square root of left parenthesis 3 right parenthesis squared plus left parenthesis negative 2 right parenthesis squared plus left parenthesis 6 right parenthesis squared end root space equals space square root of 9 plus 4 plus 36 end root space equals space square root of 49 space equals space 7
therefore            unit vector in the direction of straight a with rightwards arrow on top
                                      equals space fraction numerator straight a with rightwards arrow on top over denominator open vertical bar straight a with rightwards arrow on top close vertical bar end fraction space equals space 1 over 7 left parenthesis 3 straight i with hat on top space minus space 2 straight j with hat on top space plus space 6 space straight k with hat on top right parenthesis
                                     equals space 3 over 7 straight i with hat on top space minus space 2 over 7 straight j with hat on top space plus space 6 over 7 straight k with hat on top.

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